Introduction to Bayesian estimation and copula models of dependence / Arkady Shemyakin, Alexander Kniazev.

Includes index.

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Introduction to Bayesian Estimation and Copula Models of Dependence; Contents; List of Figures; List of Tables; Acknowledgments; Acronyms; Glossary; About the Companion Website; Introduction; Part I Bayesian Estimation; 1 Random Variables and Distributions; 1.1 Conditional Probability; 1.2 Discrete Random Variables; 1.3 Continuous Distributions on the Real Line; 1.4 Continuous Distributions with Nonnegative Values; 1.5 Continuous Distributions on a Bounded Interval; 1.6 Joint Distributions; 1.7 Time-Dependent Random Variables; References; 2 Foundations of Bayesian Analysis

2.1 Education and Wages2.2 Two Envelopes; 2.3 Hypothesis Testing; 2.3.1 The Likelihood Principle; 2.3.2 Review of Classical Procedures; 2.3.3 Bayesian Hypotheses Testing; 2.4 Parametric Estimation; 2.4.1 Review of Classical Procedures; 2.4.2 Maximum Likelihood Estimation; 2.4.3 Bayesian Approach to Parametric Estimation; 2.5 Bayesian and Classical Approaches to Statistics; 2.5.1 Classical (Frequentist) Approach; 2.5.2 Lady Tasting Tea; 2.5.3 Bayes Theorem; 2.5.4 Main Principles of the Bayesian Approach; 2.6 The Choice of the Prior; 2.6.1 Subjective Priors; 2.6.2 Objective Priors

2.6.3 Empirical Bayes2.7 Conjugate Distributions; 2.7.1 Exponential Family; 2.7.2 Poisson Likelihood; 2.7.3 Table of Conjugate Distributions; References; 3 Background for Markov Chain Monte Carlo; 3.1 Randomization; 3.1.1 Rolling Dice; 3.1.2 Two Envelopes Revisited; 3.2 Random Number Generation; 3.2.1 Pseudo-random Numbers; 3.2.2 Inverse Transform Method; 3.2.3 General Transformation Methods; 3.2.4 Accept-Reject Methods; 3.3 Monte Carlo Integration; 3.3.1 Numerical Integration; 3.3.2 Estimating Moments; 3.3.3 Estimating Probabilities; 3.3.4 Simulating Multiple Futures

3.4 Precision of Monte Carlo Method3.4.1 Monitoring Mean and Variance; 3.4.2 Importance Sampling; 3.4.3 Correlated Samples; 3.4.4 Variance Reduction Methods; 3.5 Markov Chains; 3.5.1 Markov Processes; 3.5.2 Discrete Time, Discrete State Space; 3.5.3 Transition Probability; 3.5.4 "Sun City"; 3.5.5 Utility Bills; 3.5.6 Classification of States; 3.5.7 Stationary Distribution; 3.5.8 Reversibility Condition; 3.5.9 Markov Chains with Continuous State Spaces; 3.6 Simulation of a Markov Chain; 3.7 Applications; 3.7.1 Bank Sizes; 3.7.2 Related Failures of Car Parts; References

4 Markov Chain Monte Carlo Methods4.1 Markov Chain Simulations for Sun City and Ten Coins; 4.2 Metropolis-Hastings Algorithm; 4.3 Random Walk MHA; 4.4 Gibbs Sampling; 4.5 Diagnostics of MCMC; 4.5.1 Monitoring Bias and Variance of MCMC; 4.5.2 Burn-in and Skip Intervals; 4.5.3 Diagnostics of MCMC; 4.6 Suppressing Bias and Variance; 4.6.1 Perfect Sampling; 4.6.2 Adaptive MHA; 4.6.3 ABC and Other Methods; 4.7 Time-to-Default Analysis of Mortgage Portfolios; 4.7.1 Mortgage Defaults; 4.7.2 Customer Retention and Infinite Mixture Models; 4.7.3 Latent Classes and Finite Mixture Models